We report on a dramatic order-of-magnitude increase in flow velocity within pinned evaporating droplets toward the end of their lifetime. The measurements were performed using high-speed microparticle image velocimetry. The study revealed interesting observations about the spatial and temporal evolution of the velocity field. The profile along the radius of the droplet is found to exhibit a maximum toward the three phase contact line with flow oscillations in time in this region. Additional optical measurements allowed further analysis of the observed trends. Analysis of the potential mechanisms responsible for the flow within the droplet demonstrated that these observations can be satisfactorily explained and accounted for by mass conservation within the droplet to compensate for evaporation.